Question

In: Physics

A wave on a string is described by y(x,t)=( 4.0 cm )×cos[2π(x/( 2.4 m )+t/( 0.30...

A wave on a string is described by y(x,t)=( 4.0 cm )×cos[2π(x/( 2.4 m )+t/( 0.30 s ))] , where x is in m and t is in s. Part B What is the wave speed? Express your answer in meters per second. Part C What is the wave frequency? Express your answer in hertz. Part D What is the wave length? Express your answer in meters. Part E At t = 0.75 s , what is the displacement of the string at x = 0.20 m ? Express your answer in centimeters.

Expert Solution

We know that

y(x,t) =A cos(kx+wt). ....1

part B) We know that the wave speed

v=w/k

comparing equation 1 from the given equation so w=2/T=2/0.30s , k=2/ =2/2.4 m

v=(2/0.30s)/(2/2.4 m)

v=8.0 m/s answer

part C) The wave frequency

f=1/T

f=1/0.30

f =3.33 Hz

part D) As you know , k=2/ =2/2.4 m

=2.4 m Answer

part E)

y(x,t)=( 4.0 cm )×cos[2π(x/( 2.4 m )+t/( 0.30 s ))]

here x=0.20 m , t=0.75 s

y(x,t)=( 4.0 cm )×cos[2π(0.20/( 2.4 m )+0.75/( 0.30 s ))]

y(x,t)=-3.464 cm

genius_generous answered 2 years ago

The wave function for a harmonic wave on a string is y(x, t) = (0.0010 m)...

The wave function for a harmonic wave on a string is y(x, t) = (0.0010 m) sin((69.8 m-1)x + (309 s-1)t). (a) In what direction does this wave travel? +x-x What is its speed? m/s (b) Find the wavelength of this wave. m Find its frequency. Hz Find its period. s (c) What is the maximum speed of any string segment? m/s

The displacement of a wave traveling in the negative x-direction is y(x,t)= ( 5.2 cm )cos(...

The displacement of a wave traveling in the negative x-direction is y(x,t)= ( 5.2 cm )cos( 6.0 x+ 73 t), where x is in m and t is in s. What is the frequency of this wave? What is the wavelength of this wave? What is the speed of this wave?

A wave on a string is described by the following equation: y = 115 cm2 cos...

A wave on a string is described by the following equation: y = 115 cm2 cos ((pi/5.0 cm) x – (pi/12 s)t) (a) What is the amplitude of this wave? (b) What is its wavelength? (c) What is its period? (d) What is its speed? (e) In which direction does the wave travel?

A certain transverse wave is described by y(x,t)=Bcos[2π(xL−tτ)], where B = 5.40 mm , L =...

A certain transverse wave is described by y(x,t)=Bcos[2π(xL−tτ)], where B = 5.40 mm , L = 28.0 cm , and τ = 4.00×10−2 s . a)Determine the wave's wavelength. b)Determine the wave's speed of propagation

A wave in a string has a wave function given by: y (x, t) = (0.0300m)...

A wave in a string has a wave function given by: y (x, t) = (0.0300m) sin [(5.35 m^-1) x + (1.63 s^-1) t] where t is expressed in seconds and x in meters. Determine: a) the amplitude of the wave b) the frequency of the wave c) wavelength of the wave d) the speed of the wave

The function y(x, t) = (20.0 cm) cos(πx - 17πt), with x in meters and t...

The function y(x, t) = (20.0 cm) cos(πx - 17πt), with x in meters and t in seconds, describes a wave on a taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement y = +17.0 cm? Number Enter your answer in accordance to the question statement Units Choose the answer from the menu in accordance to the question statement This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2...

The wave function for a traveling wave on a taut string is (in SI units) y(x,t)...

The wave function for a traveling wave on a taut string is (in SI units) y(x,t) = 0.375 sin (14pt - 2px + p/4) (a) What are the speed and direction of travel of the wave? speed _____ m/s direction_________ (positive x-direction, positive y-direction, positive z-direction, negative x-direction, negative y-direction, negative z-direction) (b) What is the vertical position of an element of the string at t = 0, x = 0.178 m? ________m (c) What is the wavelength of the...

Let f (t) = { 7 0 ≤ t ≤ 2π cos(5t) 2π < t ≤ ...

Let f (t) = { 7 0 ≤ t ≤ 2π cos(5t) 2π < t ≤ 4π e3(t−4π) t > 4π (a) f (t) can be written in the form g1(t) + g2(t)U(t − 2π) + g3(t)U(t − 4π) where U(t) is the Heaviside function. Enter the functions g1(t), g2(t), and g3(t), into the answer box below (in that order), separated with commas. (b) Compute the Laplace transform of f (t).

A sinusoidal wave in a string is described by the wave function y = 0.155 sin...

A sinusoidal wave in a string is described by the wave function y = 0.155 sin (0.525x - 46.5t) where x and y are in meters and t is in seconds. The mass per length of the string is 13.2 g/m. (a) Find the maximum transverse acceleration of an element of this string. (b) Determine the maximum transverse force on a 1.00-cm segment of the string. (c) State how the force found in part (b) compares with the tension in...

A mechanical wave is given by the equation: y(x,t) = 0.5 cos (62.8x – 15.7t) ,...

A mechanical wave is given by the equation: y(x,t) = 0.5 cos (62.8x – 15.7t) , Find: (1) Amplitude, frequency, wavelength? (2) The velocity of the wave? (3) The maximum velocity of the vibrations? (4) Write down the equation in the opposite direction?